Abstract

The invariance with motion of the measurement of two-way light signals in the Michelson-Morley experiment is extrapolated to one-way measurements. The time of arrival of signals at a distant point is accepted as indeterminate, in accordance with the before-and-after characterization of Robb; but it is shown that, in spite of this indeterminancy, definite expressions can be obtained for the operations involved in measuring one-way signals. Extension of the same reasoning leads to Lorentz-type transformations expressed in terms of observable rod and clock readings, which include the self-observed velocities of moved clocks used to set the epochs of distant clocks.

© 1950 Optical Society of America

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Corrections

Herbert E. Ives, "Errata*: Extrapolation from the Michelson-Morley Experiment," J. Opt. Soc. Am. 40, 883_3-883 (1950)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-40-12-883_3

References

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  1. I. Newton, Mathematical Principles, translated by F. Cajori (University of California Press, Berkeley, 1946), Corollary V, p. 20.
  2. A. A. Robb, A Theory of Space and Time (Cambridge University Press, London, 1914).
  3. A. Einstein, Ann. d. Physik 4, 891 (1905).
    [Crossref]
  4. H. E. Ives, J. Opt. Soc. Am. 39, 757 (1949).
    [Crossref]
  5. H. E. Ives, Phil. Mag. 36, 392 (1945).
  6. H. E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938); J. Opt. Soc. Am. 31, 369 (1941). In these experiments the conditions of test correspond to the use of setting clocks moved at negligible velocities, since the velocities of the canal rays were obtained from their Doppler effects, using tke value c for the velocity of light.
    [Crossref]

1949 (1)

1945 (1)

H. E. Ives, Phil. Mag. 36, 392 (1945).

1938 (1)

1905 (1)

A. Einstein, Ann. d. Physik 4, 891 (1905).
[Crossref]

Ann. d. Physik (1)

A. Einstein, Ann. d. Physik 4, 891 (1905).
[Crossref]

J. Opt. Soc. Am. (2)

Phil. Mag. (1)

H. E. Ives, Phil. Mag. 36, 392 (1945).

Other (2)

I. Newton, Mathematical Principles, translated by F. Cajori (University of California Press, Berkeley, 1946), Corollary V, p. 20.

A. A. Robb, A Theory of Space and Time (Cambridge University Press, London, 1914).

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Figures (1)

Fig. 1
Fig. 1

Light-signal and clock-at-origin relations on initial and relatively moving platforms.

Equations (41)

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t 0 + t b = 2 D / c .
t 0 = ( D / c ) - F ,
t b = ( D / c ) + F ,
t 0 = d / c 0 ,
t b = d / c b ,
t 0 + t b = d [ ( c 0 + c b ) / c 0 c b ] .
d [ ( c 0 + c b ) / c 0 c b ] = 2 d / c
( c 0 + c b ) / c 0 c b = 2 / c .
D + W t 0 = c 0 t 0
D - W t b = c b t b .
t = t 0 + t b = D [ ( c 0 + c b ) / c 0 c b ] / [ 1 - ( W / c 0 ) ] [ 1 + ( W / c b ) ] .
D i = D f D ( W )
t i = ( t 0 + t b ) i = ( t 0 + t b ) + f T ( W ) = t / f T ( W )
t = D [ ( c 0 + c b ) / c 0 c b ] f D ( W ) f T ( W ) / [ 1 - ( W / c 0 ) ] [ 1 + ( W / c b ) ] .
f D ( W ) f T ( W ) = ( 1 - W c 0 ) ( 1 + W c b ) ,
t = ( t 0 + t b ) = D [ ( c 0 + c b ) / c 0 c b ] = 2 D / c ,
Y = D i / τ i = D f D ( W ) f T ( W ) τ ,
Y = D i / τ i = q f D ( W ) f T ( W + Y ) .
Δ = τ i f T ( W ) - τ .
D i / τ i = Y D i = D f D ( W ) D / τ = q ,
Δ = D f D ( W ) f T ( W ) Y - D q .
t = t i f T ( W ) - Δ .
t 0 = D f D ( W ) f T ( W ) c 0 - W - D f D ( W ) f T ( W ) Y + D q = D c 0 + D W c 0 c b - D f D ( W ) f T ( W ) Y + D q .
K = D W c 0 c b - D f D ( W ) f T ( W ) Y .
Y = D f D ( W ) f T ( W ) ( D W / c 0 c b ) - K .
D ( D W / c 0 c b ) - K = q f T ( W + Y ) f T ( W ) = q f D ( W + Y ) f T ( W + Y ) f T ( W ) f D ( W + Y ) = q { [ 1 - ( W + Y / c 0 ) ] } { [ 1 + ( W + Y ) / c b ] } f T ( W ) f D ( W + Y ) .
D 2 q 2 = f D ( W ) f T ( W + Y ) f T ( W ) f D ( W + Y ) ( K + D c 0 ) ( K - D c b ) .
D 2 q 2 = ( K + D c 0 ) ( K - D c b ) .
K = - D c + D c b ± D q ( 1 + q 2 c 2 ) 1 2 .
t 0 = ( D / c 0 ) + K + ( D / q ) ,
t 0 = D c ± D q ( 1 + q 2 c 2 ) 1 2 + D q .
t 0 = D c - D q [ ( 1 + q 2 c 2 ) 1 2 - 1 ] .
t b = ( t 0 + t b ) - t 0 = 2 D c - D c + D q [ ( 1 + q 2 c 2 ) 1 2 - 1 ] = D c + D q [ ( 1 + q 2 c 2 ) 1 2 - 1 ] .
F = D [ ( 1 + q 2 c 2 ) 1 2 - 1 ] / q ,
f D ( W ) f T ( W + Y ) f T ( W ) f D ( W + Y )
[ f T ( Y ) / f D ( Y ) ] = 1 ,
f D ( W ) = f T ( W ) = [ ( 1 - W c 0 ) ( 1 + W c b ) ] 1 2 .
f D ( W ) = f T ( W ) = ( 1 - W c 0 + W c b - W 2 c 0 c b ) 1 2
f D ( W ) f T ( W ) = 1 - ( W 2 / c 2 ) .
f D ( W ) = f T ( W ) = [ 1 - ( W 2 / c 2 ) ] 1 2 ,
D t = c 1 ± ( c / q ) { [ 1 + ( q 2 / c 2 ) ] 1 2 - 1 } .